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Question #27560

****comma indicates a new row****
Show that the 2x2 matrix S = [0 1, -1 0] is real, normal, and has eigenvalues +-i. Show that the eigenvalues of N^TN are both one. (where T is transpose).

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**1.**k is an eigenvalue of S iff det(S-kI) = 0, and det(AB) = det(A)det(B). Please use thes…**2.**k is an eigenvalue of S iff det(S-kI) = 0, and det(AB) = det(A)det(B). Use these facts …**3.**Let * equal conjugate transpose. Given a Hermitian Matrix H, show that the eigenvalues…**4.**write the matrix A[3,-1,1,-2]as a linear combination of A1=[1,1,0,-1],A2=[1,1,-1,0]and …**5.**prove that if AB=BA for every N by N matrix A, then B=cI for some constant c**6.**A boy was born on his father's 30th birthday. The sum of their ages is now 40 year…**7.**If f(x) = 4x2 + 5x calculate (i) f(-2) (ii) (ii) f -1(9)

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